Question

Calculate the energies of one photon of ultraviolet (λ = 1 x 10⁻⁸ m), visible (λ = 5 x 10⁻⁷ m), and infrared (λ = 1 x 10⁴ m) light. What do the answers indicate about the relationship between the wavelength and energy of light?

Answer 1

Answer:

• Energy of ultraviolet light is 19.878 10⁻¹⁸ J

• Energy of visible light is 3.9756 X 10⁻¹⁹ J

• Energy of infrared light is 19.878 X 10⁻³⁰ J

The answers indicate that wavelength is inversely proportional to the energy of light (photon)

Explanation:

Energy of photon E = hc/λ

where;

h is Planck's constant = 6.626 X 10⁻³⁴js

c is the speed of light (photon) = 3 X 10⁸ m/s

λ is the wavelength of the photon

⇒For ultraviolet ray, with wavelength λ = 1 x 10⁻⁸ m

E = (6.626 X 10⁻³⁴ X 3 X 10⁸)/ (1 x 10⁻⁸)

E = 19.878 10⁻¹⁸ J

⇒For Visible light, with wavelength λ = 5 x 10⁻⁷ m

E = (6.626 X 10⁻³⁴ X 3 X 10⁸)/ (5 x 10⁻⁷)

E = 3.9756 X 10⁻¹⁹ J

⇒For Infrared, with wavelength λ = 1 x 10⁴ m

E = (6.626 X 10⁻³⁴ X 3 X 10⁸)/ (1 x 10⁴)

E = 19.878 X 10⁻³⁰ J

From the result above, ultraviolet ray has the shortest wavelength, but it has the highest energy among other lights.

Also infrared has the highest wavelength but the least energy among other lights.

Hence, wavelength is inversely proportional to the energy of light (photon).